Dimension reduction for model-based clustering via mixtures of shifted asymmetric Laplace distributions

A dimension reduction method for model-based clustering via a finite mixture of shifted asymmetric Laplace distributions is introduced. The approach is based on existing work within the Gaussian paradigm and relies on identification of a reduced subspace. This subspace contains linear combinations of the original data, ordered by importance using the associated eigenvalues. This clustering approach is illustrated on simulated and real data, where it performs favourably compared to its Gaussian analogue.